In a milking machine, a plurality of teatcups are connected to respective teats suspending from the udder of a mammal, such as a cow. Each teatcup assembly has a teatcup liner or inflation around a respective teat and defining a milk flow passage within the liner below the teat, and a pulsation chamber outside the liner between the liner and a teatcup shell. The system has a milking cycle with an on portion and an off portion. Milk flows from the teat towards a milking claw during the on portion, and then to a storage vessel. During the off portion, the liner is collapsed around the teat, to aid in the circulation of body fluids. Vacuum pressure is continuously applied to the milk flow passage within the liner. Vacuum and ambient pressure are alternately and cyclically applied to the pulsation chamber between the liner and the teatcup shell, to open and close the liner.